According to Dubrovin's conjecture, the Stokes structure of the quantum D module of a Fano manifold is described by a semi-orthogonal decomposition of the derived category of coherent sheaves. 

When a torus acts on a Fano manifold, the equivariant quantum D module is equipped with shift operators. 

In this talk, I will explain an attempt to formulate an equivariant analogue of Dubrovin's conjecture.